function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta

h = sigmoid(X * theta);
n = length(theta);
J = -1/m * ( (y)' * log(h) + (1-y)' * log(1-h) ) + lambda/(2*m) * (theta(2:n)'*theta(2:n));
grad(1) = 1/m * (h-y)' * X(:,1);
grad(2:n) = (1/m* (h-y)' * X(:, 2:n)) .+ (lambda/m * theta(2:n)');


% =============================================================

end
